ordered integral domain in English

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{
  "forms": [
    {
      "form": "ordered integral domains",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "ordered integral domain (plural ordered integral domains)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
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          "source": "w"
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        {
          "kind": "topical",
          "langcode": "en",
          "name": "Algebra",
          "orig": "en:Algebra",
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        }
      ],
      "glosses": [
        "An integral domain which has a subset whose elements are said to be \"positive\", such that this subset is closed under addition, closed under multiplication, and all elements of the integral domain satisfy a law of trichotomy; namely, that either that element is in the said subset, or it is the zero (additive identity), or its product with −1 (the additive inverse of the multiplicative identity) belongs to the said subset."
      ],
      "hyponyms": [
        {
          "word": "ordered field"
        }
      ],
      "id": "en-ordered_integral_domain-en-noun-sLv1Sbsv",
      "links": [
        [
          "algebra",
          "algebra"
        ],
        [
          "integral domain",
          "integral domain"
        ],
        [
          "trichotomy",
          "trichotomy"
        ]
      ],
      "raw_glosses": [
        "(algebra) An integral domain which has a subset whose elements are said to be \"positive\", such that this subset is closed under addition, closed under multiplication, and all elements of the integral domain satisfy a law of trichotomy; namely, that either that element is in the said subset, or it is the zero (additive identity), or its product with −1 (the additive inverse of the multiplicative identity) belongs to the said subset."
      ],
      "topics": [
        "algebra",
        "mathematics",
        "sciences"
      ]
    }
  ],
  "word": "ordered integral domain"
}

[Show JSON for raw wiktextract data ▼] [Hide JSON for raw wiktextract data ▲]

{
  "forms": [
    {
      "form": "ordered integral domains",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "ordered integral domain (plural ordered integral domains)",
      "name": "en-noun"
    }
  ],
  "hyponyms": [
    {
      "word": "ordered field"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        "English countable nouns",
        "English entries with incorrect language header",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "en:Algebra"
      ],
      "glosses": [
        "An integral domain which has a subset whose elements are said to be \"positive\", such that this subset is closed under addition, closed under multiplication, and all elements of the integral domain satisfy a law of trichotomy; namely, that either that element is in the said subset, or it is the zero (additive identity), or its product with −1 (the additive inverse of the multiplicative identity) belongs to the said subset."
      ],
      "links": [
        [
          "algebra",
          "algebra"
        ],
        [
          "integral domain",
          "integral domain"
        ],
        [
          "trichotomy",
          "trichotomy"
        ]
      ],
      "raw_glosses": [
        "(algebra) An integral domain which has a subset whose elements are said to be \"positive\", such that this subset is closed under addition, closed under multiplication, and all elements of the integral domain satisfy a law of trichotomy; namely, that either that element is in the said subset, or it is the zero (additive identity), or its product with −1 (the additive inverse of the multiplicative identity) belongs to the said subset."
      ],
      "topics": [
        "algebra",
        "mathematics",
        "sciences"
      ]
    }
  ],
  "word": "ordered integral domain"
}

This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-05-03 from the enwiktionary dump dated 2024-05-02 using wiktextract (f4fd8c9 and c9440ce). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.

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"ordered integral domain" meaning in English

Noun

Inflected forms